Advanced Calculus: Second Edition

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Patrick M. Fitzpatrick

Advanced Calculus is intended as a text for courses that furnish
the backbone of the student's undergraduate education in mathematical
analysis. The goal is to rigorously present the fundamental concepts
within the context of illuminating examples and stimulating exercises.
This book is self-contained and starts with the creation of basic tools
using the completeness axiom. The continuity, differentiability,
integrability, and power series representation properties of functions of
a single variable are established. The next few chapters describe the
topological and metric properties of Euclidean space. These are the basis
of a rigorous treatment of differential calculus (including the Implicit
Function Theorem and Lagrange Multipliers) for mappings between Euclidean
spaces and integration for functions of several real variables.

Special attention has been paid to the motivation for proofs. Selected
topics, such as the Picard Existence Theorem for differential equations,
have been included in such a way that selections may be made while
preserving a fluid presentation of the essential material.

Supplemented with numerous exercises, Advanced Calculus is a
perfect book for undergraduate students of analysis.

An instructor's manual for this title is available electronically. Please
send email to textbooks@ams.org for more
information.

Readership

Undergraduate students interested in teaching and learning
undergraduate analysis.

Reviews & Endorsements

This is
a well-written and well-structured book with clearly explained proofs and a
good supply of exercises, some of them are quite challenging. It is this
reviewer's opinion that the volume should be an excellent and useful tool for
undergraduate students.

Advanced Calculus is intended as a text for courses that furnish
the backbone of the student's undergraduate education in mathematical
analysis. The goal is to rigorously present the fundamental concepts
within the context of illuminating examples and stimulating exercises.
This book is self-contained and starts with the creation of basic tools
using the completeness axiom. The continuity, differentiability,
integrability, and power series representation properties of functions of
a single variable are established. The next few chapters describe the
topological and metric properties of Euclidean space. These are the basis
of a rigorous treatment of differential calculus (including the Implicit
Function Theorem and Lagrange Multipliers) for mappings between Euclidean
spaces and integration for functions of several real variables.

Special attention has been paid to the motivation for proofs. Selected
topics, such as the Picard Existence Theorem for differential equations,
have been included in such a way that selections may be made while
preserving a fluid presentation of the essential material.

Supplemented with numerous exercises, Advanced Calculus is a
perfect book for undergraduate students of analysis.

An instructor's manual for this title is available electronically. Please
send email to textbooks@ams.org for more
information.

Undergraduate students interested in teaching and learning
undergraduate analysis.

Reviews:

This is
a well-written and well-structured book with clearly explained proofs and a
good supply of exercises, some of them are quite challenging. It is this
reviewer's opinion that the volume should be an excellent and useful tool for
undergraduate students.